Cutoff for geodesic paths on hyperbolic manifolds
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910189875101696 |
|---|---|
| author | Bordenave, Charles Mathien, Joffrey |
| author_facet | Bordenave, Charles Mathien, Joffrey |
| contents | We establish new instances of the cutoff phenomenon for geodesic paths and for the Brownian motion on compact hyperbolic manifolds. We prove that for any fixed compact hyperbolic manifold, the geodesic path started on a spatially localized initial condition exhibits cutoff. Our work also extends results obtained by Golubev and Kamber on hyperbolic surfaces of large volume to any dimension. Our proof builds upon a spectral strategy introduced by Lubetzky and Peres for Ramanujan graphs and on a detailed spectral analysis of the spherical mean operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cutoff for geodesic paths on hyperbolic manifolds Bordenave, Charles Mathien, Joffrey Probability Geometric Topology We establish new instances of the cutoff phenomenon for geodesic paths and for the Brownian motion on compact hyperbolic manifolds. We prove that for any fixed compact hyperbolic manifold, the geodesic path started on a spatially localized initial condition exhibits cutoff. Our work also extends results obtained by Golubev and Kamber on hyperbolic surfaces of large volume to any dimension. Our proof builds upon a spectral strategy introduced by Lubetzky and Peres for Ramanujan graphs and on a detailed spectral analysis of the spherical mean operator. |
| title | Cutoff for geodesic paths on hyperbolic manifolds |
| topic | Probability Geometric Topology |
| url | https://arxiv.org/abs/2502.06325 |